Evaluate ^ -1 ( )dx - Vidyadip

Question

Evaluate $\int\cos^{-1}(\sin\text{x})\text{dx}$

✓

Answer

$\int\cos^{-1}(\sin\text{x})\text{dx}=\int\cos^{-1}\Big(\cos\Big(\frac{\pi}{2}-\text{x}\Big)\Big)\text{dx}$
$=\int\Big(\frac{\pi}{2}-\text{x}\Big)\text{dx}$
$=\frac{\pi}{2}\text{x}-\frac{1}{2}\text{x}^2+\text{C}$
Hence, $\int\cos^{-1}(\sin\text{x})\text{dx}=\frac{\pi}{2}\text{x}-\frac{1}{2}\text{x}^2+\text{C}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "Solve the Following Question.(2 Marks)" from Indefinite Integrals→Indefinite Integrals — all question types→Maths STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

Find the derivative of the inverse function of the following

$y=x^2 \cdot e^x$

If $\bar{a}=3 \hat{i}-2 \hat{j}+7 \hat{k}, \bar{b}=5 \hat{i}+\hat{j}-2 \hat{k}$ and $\bar{c}=\hat{i}+\hat{j}-\hat{k}$ then find $\bar{a} \cdot(\bar{b} \times \bar{c})$

Show that the following systems of linear equations has infinite number of solutions and solve:

Evaluate the following:
$\sin\Big(\frac{1}{2}\cos^{-1}\frac{4}{5}\Big)$

Find the condition that : the line $4 x+5 y=0$ coincides with one of the lines given by ax ${ }^2+2 h x y+b y^2=0$.

Diffrentiate the following w.r.t.x

$\sec \left[\tan \left(x^4+4\right)\right]$

Diffrentiate the following w.r.t.x

$\sqrt{e^{(3 x+2)}+5}$

Write rthe value of the determinant $\begin{vmatrix}\text{p}&\text{p}+1\\\text{p}-1&\text{p}\ \end{vmatrix}$

If the normal to the plane has direction ratios 2, −1, 2 and it’s perpendicular distance from origin is 6, find its equation

Find the position vector of the min-point of the line segment AB, where A is the point (3, 4, -2) and B is the point (1, 2, 4).